Is one allowed to tear off leaves from fresh myrtle branches that are in a vase on Shabbos?
It is permitted. The prohibition not to rip off leaves (Mileches Kotzair) is only when they are attached to the ground, which is their source of growth, but after they were already cut and detached from the ground, the place where they grew, the prohibition no longer is applicable.
It should be noted, that even though fresh flowers that will still bloom should not be put into a vase, it is premitted to take them out. Additionally with myrtle branches there aren’t any flowers that might bloom as a result, therfore even putting it into water would be permitted. see Nishmas Avrohom OI:CH 336-1, Kovetz Mbais Levi 6 pg. 478 (11), KOvetz halachos (Shavuos) 11 ftnt. 5.